Fracture Mechanics of Solder Bumps During Ball Shear Testing: Effect of Bump Size

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1 Journal of ELECTRONIC MATERIALS DOI: /s z Ó 2009 TMS Regular Issue Paper Fracture Mechanics of Solder Bumps During Ball Shear Testing: Effect of Bump Size WOONG HO BANG, 1 CHOONG-UN KIM, 1,3 SUK HOON KANG, 2 and KYU HWAN OH 2 1. Department of Materials Science and Engineering, University of Texas, Arlington, TX 76019, USA. 2. School of Materials Science and Engineering, Seoul National University, Seoul , Korea choongun@uta.edu This paper examines the mechanics of ball shear testing with the objective of understanding the mechanism by which the maximum shear force and the rate of crack growth is dependent on the solder bump size. For this, Pb-Sn solder bumps with diameters between 460 lm and 760 lm are soldered to 400 lm-diameter Cu pads and subjected to ball shear testing. In spite of the constant interface area, the bump size significantly impacts the measured shear fracture force and the crack growth rate. Both the fracture force and the crack growth rate increase with bump size, and in the case of the fracture force, the increase is almost linear. Our analysis finds that the linear increase in the fracture force is a result of the bump deformation force, which increases with bump size. A simple model that accounts for the deformation force component is developed and used to extract the true interface fracture force. The estimated true interface fracture force is found to vary little with bump size, tightly converging to the 40 MPa to 48 MPa range. On the other hand, the dependence of crack growth rate on bump size is found to result from the higher degree of rotational moment associated with larger bumps. Key words: Ball shear testing, solder bump size, shear fracture force, crack growth rate, bump deformation, bump rotation INTRODUCTION The ball shear test has gained considerable popularity as a method of assessing the mechanical reliability of solder joints because it is relatively simple to perform yet provides data predictive of joint reliability. The method is based on a fairly simple configuration and test procedure. In this test, a rigid shear probe makes contact with a solder bump from the side and induces displacement of the solder bump in a direction parallel to the solder/ metallization interface until failure. 1 The maximum force is usually taken as meaningful data and is used as a comparative index indicating the integrity of the solder joint. In addition to the comparative index, there are continuing attempts to use the (Received February 10, 2009; accepted April 30, 2009) resulting data in a more quantitative manner, that is, directly relating the measured shear strength to the interfacial fracture strength. Since the predominant place for cracking in a ball shear test is the solder/metallization interface, it may not seem unreasonable to correlate the measured shear strength with the interfacial fracture strength. 2 8 Nevertheless, with limited studies on the fracture mechanics aspect of ball shear testing, the validity of such a correlation is still not clear. The desire to extract more fundamental information from the ball shear test is spurred by the facts that (1) the interface strength is one of the most critical, yet most difficult, properties to characterize in the assessment of joint reliability and (2) the ball shear test configuration appears to be ideal for providing such data. 2 8 However, our recent study found that the fracture mechanics in a ball shear test are not as ideal as first appears. 9 In the

2 Bang, Kim, Kang, and Oh previous study, we found several factors that may complicate the fracture behavior of solder bumps during ball shear testing. Such factors include plasticity and physical bump rotation during the fracture process, 9 13 both of which suggest that the test result may vary significantly with the configuration of the ball. In order to better utilize the solder ball shear test, it is clear that more needs to be understood about its fracture mechanics. Of many possible experiments and numerical simulations that may be used to investigate fracture mechanics in the ball shear test, we have chosen to examine the changes in the fracture characteristics of various ball sizes while keeping the Cu/solder interface area the same. With ball size the only variable, any difference in fracture characteristics can be attributed to the influence of ball rotation and plasticity on the crack propagation. For this, shear tests of various bump sizes having identical interface area are carried out and also analyzed using finite element method (FEM) numerical analysis. The results indicate that the fracture characteristics of the bump are indeed influenced greatly by the bump size. Specifically, it is found that cracks in larger bumps propagate faster but require higher shear force. The reason for the higher shear force requirement for larger bumps is related to the fact that a greater portion of the applied shear force is absorbed by the compression deformation of the solder at the probe contact. On the other hand, once it starts, crack propagation occurs more rapidly in larger bumps because a greater degree of rotational moment, and thus body rotation, creates faster stress intensity factor development at the crack tip. The results suggest that the ball shear test is useful in identifying potential reliability risks because it tests the interface under the most severe fracture condition, but a quantitative measure of interface fracture strength must be extracted with care because the fracture is not solely affected by interface strength but also by bump geometry. This paper details the experimental evidence and theoretical analysis leading to such conclusions. EXPERIMENTAL PROCEDURES AND NUMERICAL ANALYSIS Experimental Procedure In order to create solder bump samples with an identical contact area, 5 lm-thick 400 lm-diameter Cu pads were defined on a FR4 board. Then, Pb-Sn eutectic solder balls of various diameters, 457 lm to 760 lm, were placed on the Cu pads and reflowed (preheat at 160 C to 183 C for 60 s then reflowed at 183 C to 220 C for 60 s). To enhance uniformity of the interface reaction, and thus, increase the reliability of test results, activation flux was applied on copper pads before the reflow process. The samples were tested using a microshear tester (Rhesca PTR- 1000) with a shear tip made of high-strength steel, which for our purposes, has negligibly small deformation. Also, since interface metallurgy may change during storage due to continued reaction at the interface, samples were tested almost immediately after their preparation. 2 8 Solder bumps were individually sheared by the probe at a constant displacement speed of 200 lm/s. More than 20 samples per bump size were tested. Numerical Analysis of Fracture Mechanics In order to better understand the variation of fracture characteristics with bump size, fracture mechanics in the bump under shear load was analyzed using FEM, primarily by estimating the stress intensity factors at the crack tip, namely, the crackopening mode, K I, and the crack-shearing mode, K II. 14 The mesh structure used for FEM analysis is shown in Fig. 1. It can be seen that our numerical analysis is carried out on a model structure consisting of a shear probe and half cross-section of a eutectic Sn-Pb/Cu bump. A crack of predefined length is assumed to be located at the most likely place for crack initiation, the neck edge bump corner (dashed circle area in Fig. 1a) within the intermetallic compound (IMC) layer. The shearing of the bump is simulated by displacing the shear probe element toward the bump by a predefined amount; then the stress intensity factors, K, are calculated at the crack tip mesh in Fig. 1b. Generally, K values are calculated at five finite-element Fig. 1. Graphical representation showing the finite element model and crack-tip mesh for fracture mechanics analysis used in this study. In this model, only bump diameter, D, is variable while other parameters are fixed at constant values to investigate the bump-size effect: (a) FEM mesh for the simulation of ball shear tests at bump diameters between D = 477 lm and 766 lm (refer to Table II); (b) microsized crack-tip mesh in IMC layer at bump corner, the dashed circle area in (a). Crack-opening K I and crack-shearing K II modes are calculated at the crack tip, but crack-tearing K III is excluded as it is not an expected crack-tip motion in the ball shear test configuration.

3 Fracture Mechanics of Solder Bumps During Ball Shear Testing: Effect of Bump Size Table I. Mechanical Properties Used in FEM Analysis 21 Elastic Modulus (GPa) Poisson s Ratio (m) Copper Cu 6 Sn Eutectic Sn-Pb FR4 substrate Steel shear bar contours surrounding the crack front from one crack face to the opposite crack face. 15 The mechanical properties used in our FEM analysis are given in Table I. Our calculation also includes plasticity of eutectic Sn-Pb having a yield strength of 35 MPa with an assumption of negligible work hardening during the shear test RESULTS Overview of Ball Shear Test Results Figure 2 presents the shear force as a function of displacement measured during ball shear tests of bumps of three different diameters. The results show that the shear force displacement relationship is not identical, but rather differs significantly with bump size. The first noticeable variation is the fact that the maximum shear force, which we name the apparent fracture force (AFF), increases with increasing bump size. Figure 3, where the AFF is displayed as a function of bump size, clearly shows that it increases almost linearly with bump size. The second variation can be found in the rate of drop in force after its maximum, which is associated with the fracture rate. Notice that, after the force maxima, the shear load per displacement drops more quickly in larger bumps. The entire set of test data, 20 per bump size, produce consistent data, as shown in Fig. 2, giving a strong indication that the fracture mechanics differs with differing bump size. This belief is reinforced by inspection of fracture surfaces after testing. As shown in Fig. 4, a scanning electron microscopy (SEM) fractograph of a typical 610 lm bump, the fracture is found to occur consistently along the interface between IMC and solder, regardless of the bump size. Thus, variation in fracture path is eliminated as a possible source of the bump-size dependence of AFF and rate shown in Fig. 2. Because the Cu pad area is kept constant for all bumps tested here, it is reasonable to conclude that the variations in fracture behavior shown in Fig. 2 are not related to variation in interface fracture strength. In a displacement-controlled fracture process such as the ball shear test, the AFF marks the initiation of continuous crack growth, while the force per displacement after the AFF represents the rate of crack growth. 14,22 The force required for a Fig. 2. Representative data showing the shear force as a function of displacement for different bump sizes. For better recognition, the maximum shear force, which is defined as AFF in this study and summarized again in Fig. 3, is highlighted with a dotted circle for each of the flow curves. Fig. 3. A plot showing the maximum shear force (AFF, refer to Fig. 2) as a function of bump diameter. The maximum shear fracture force presented in this plot is an average of 20 measurements. The linear fitting was made based on least-squares principles. given displacement increases until the stress intensity factor, K, at the crack tip reaches the critical value for continuous crack growth, and at this moment, if interface area is the same and if the interface strength alone determines the maximum force, the AFF should be independent of bump size. However, our finding reveals that the AFF changes with bump size, suggesting that it is the sum of the interface fracture force and a force that varies with bump size. Similarly, the bump size dependence of force reduction per displacement after AFF suggests that the crack growth rate is also affected by the bump size. As detailed in the following sections, our experimental and FEM fracture analysis find that the dependence of AFF and crack growth rate on

4 Bang, Kim, Kang, and Oh Fig. 4. SEM micrograph of the fracture surface of a 610 lm bump after the shear test. As shown in the inset, the crack propagation is found to occur predominantly along the interface between IMC and solder. bump size occurs due to plastic deformation of solder at the probe tip and bump rotation during the fracture process. Solder Deformation and Fracture Force Development In a ball shear test, solder plastically deforms at the contact point between the solder and the probe tip. An example of such deformation is shown in Fig. 5, where SEM images of solder bumps after shearing to two prescribed distances are presented. These micrographs show the presence of a flattened area, evidencing the occurrence of extensive compressive plastic deformation. If, as these images suggest, a significant portion of the applied force goes into plastic deformation at the contact point, a smaller force is transmitted to the crack tip. They further suggest that the AFF dependence on bump size (Fig. 3) may be attributed to the dependence of the contact deformation force on bump size. The impact of bump size on the AFF can be examined if the force for contact deformation at the time of fracture can be determined. The applied force should consist of the force for bump deformation and the true interface fracture force: AFF ¼ F a ðu f Þ F d ðu f ÞþF i ; (1) where U f is the displacement at fracture, F a represents the applied force at the probe tip, and F d and F i are the force for contact deformation and the interface fracture force, respectively. Here, the force for partial interfacial failure during the crack nucleation period is ignored because its contribution should be negligibly small. Since the interface fracture force should be independent of bump size in Fig. 5. SEM micrographs showing deformation of a 610 lm bump at the probe contact at two different displacements: (a) 50 lm; (b) after complete shear to failure. The black arrows in the micrographs indicate the shear direction and resulting compressive deformation at bump body. The white arrow in (b) emphasizes fracture at the interface area by complete shearing. our test configuration, the bump size affects the AFF by influencing the deformation force. While an exact determination of the contact deformation force is nearly impossible, a rough estimate can be made using a few simplifications. Assuming a negligible contribution from elastic deformation, the contact deformation force at displacement position U can be expressed as 23 F d ðu Þ ¼ r Y ðuþau ð Þ; (2) where r Y (U) is the yield strength of the solder matrix and A(U) is the contact area between the bump and shear probe. For simplicity, the yield strength can be assumed to be constant. This assumption does not create significant error in our analysis because most solder alloys have a very low workhardening rate in the range of strain rates relevant to bump shear testing The contact area, A(U), can be estimated by extending the result from the Abbott-Firestone contact curve model

5 Fracture Mechanics of Solder Bumps During Ball Shear Testing: Effect of Bump Size According to the Abbott-Firestone model, the contact area between a fully plastic sphere and a rigid flat surface can be approximated as the product of the circumference before deformation and the displacement from the sphere edge: AU ð Þ ¼ p D s U; (3) where D s is the initial sphere diameter before deformation. Our analysis finds that Eq. 3 can also be applied to the case of a solder bump, even though the shape of the solder bump is not a perfect sphere. When we consider the exact shape of a solder bump and compute the contact area, use of Eq. 3 creates an error of less than 3%. Therefore, the deformation force at a given displacement U can be approximated as F d ðuþ p r Y D b U: (4) Here, D b represents the initial bump diameter. Consequently, the deformation force at the time of fracture initiation becomes F d ðu f Þ p r Y D b U f : (5) Equation 5 reveals a few points of importance in understanding the fracture mechanics of the ball shear test. First, Eq. 5 indicates that, for the given solder alloy, the force for contact deformation is affected only by the bump diameter and the fracture displacement. In the case when the fracture displacement does not vary much with the bump diameter, the deformation force, and thus, the AFF, should linearly increase with the bump diameter. As evidenced in Table II, which presents a summary of experimentally measured fracture displacement (U f ) for different solder bump sizes, U f is approximately 100 lm, and fairly independent of the bump size. Combined with Eqs. 1 and 5, this data explains the linearly increasing AFF with bump size (Fig. 3). Secondly, Eq. 5 suggests that the rate of increase in AFF with bump size is a linear function of the yield Table II. Summary of Data Collected from Ball Shear Testing, Including AFF, and Fracture Displacement (lm) Ball Diameter Initial Bump Diameter (D b ) a DX b Load Maximum (N) Shear Distance at Load Maximum (U f ) a Bump diameters are calculated with an assumption that the solder balls are ideally wetted on 400 lm-diameter copper metallization pad; b DX, distance between a shear probe and neck edge corner of solder (Fig. 1). strength of the given solder alloy. Since the interface fracture force F i is an independent function of the bump diameter, Eqs. 1 and 5 lead to daff ¼ df aðu f Þ ¼ df dðu f Þ pr Y U f : (6) dd b dd b dd b Because the measured fracture displacement is nearly constant, Eq. 6 indicates that the rate of linear increase in measured fracture force with bump size is determined by the yield strength of the solder alloy. The slope of the AFF increase with bump size shown in Fig. 3 is N/lm. According to Eq. 6, when U f 100 lm, this slope corresponds to r Y = 35 MPa. A yield strength of 35 MPa matches very well with the flow stress level of Pb-Sn bulk alloys in the high-strain-rate regime of conventional tensile and creep tests. 19,27 33 This agreement presents strong evidence that the deformation force analysis presented here is valid and that the fracture force measured in a ball shear test is greatly affected by the plastic deformation of the bump. Finally, the true interface fracture strength can be extracted using Eq. 1 because Eq. 5 allows determination of the deformation force for each bump, assuming r Y = 35 MPa. Application of this method to all experimental data using a U f of 100 lm yields interface fracture force values that tightly converge to 5 N to 6 N. This interface fracture force corresponds to an interface fracture strength of 40 MPa to 48 MPa. The fact that all data, even with considerable variation in AFF, yield a nearly identical interface fracture strength suggests that our analysis is correct and the resulting value may be the correct fracture strength of an interface formed by reflowing Pn-Sn solder on Cu and measured by the ball shear test method. Bump Rotation and Crack Growth The second fracture behavior that deserves further investigation is the variation in crack growth rate per displacement with bump size. As shown in Fig. 2, the force drop per displacement after the force maximum is more rapid in larger bumps. After its maximum, the shear force corresponds to the process of continuous crack propagation along the interface, and it decreases because the crack growth makes the stress intensity factor higher, resulting in lower shear force needed for continued fracture. Since the solder/cu interface is identical and the test force is applied parallel to the interface, the dependence of crack growth rate on bump size may appear odd, but suggests that a factor other than shear rate and interface fracture strength affects the rate of crack growth. Our study finds that the source of the dependency is related to the physical rotation of the bump in the shearing direction, with its rotational axis at the crack tip. The degree of bump rotation, and thus, the rate of stress intensity factor development with crack growth are found to differ with bump size,

6 Bang, Kim, Kang, and Oh Fig. 6. Micrographs showing the sequence of body rotation during shearing of 766 lm- and 477 lm-diameter solder bumps. Horizontal arrows in row (a) indicate the shear direction of a shear bar: (a) before shearing, (b) shear to 150 lm, (c) after completion of shear. Before experiments, a micro-indentation marker is made on the top to trace the center of the bump and is denoted by a vertical arrow in row (a). resulting in a keen dependence of the crack growth rate on the bump size. The evidence for bump rotation during crack growth is shown in Fig. 6, a series of snap shots of two bumps captured by a high-speed camera during ball shear testing. As indicated by an arrow in the photos, a tiny indentation is made on the top center of these bumps prior to shear testing for tracing purposes. It is evident that the indentation mark gradually rotates toward the shear direction, indicating that the entire bump is rotating in the same direction. Further evidence of body rotation can be seen from the opening of the bump interface (grey arrow) where shear force is exerted. Note that the interface opening due to bump rotation is more prominent in the larger bump (766 lm) than in the smaller bump (477 lm) (Fig. 6b). The fact that body rotation occurs during interface fracture suggests that the crack growth does not proceed in the pure shear mode (K II mode), but in combination with the crack-opening mode (K I mode). Also, the greater rotation rate in the larger bump indicates that the crack-opening stress intensity factor, K I, develops much more quickly in the larger bump, resulting in a faster crack growth than in the smaller bump. While the bump rotation is clearly evident, the source of its driving force is not clear because the only force exerted on the bump is the shear force applied parallel to the bump interface. Our present study finds that the rotation occurs because of the configuration inherent to the ball shear test. As shown in Fig. 1, the shearing force is exerted on the bump body through contact at the bump side. This means that there is a stand-free distance between the initial probe/solder contact point and the interface (denoted by DX). Because the motion of the bump is constrained at the bottom interface, exerting a shear force from this point creates a rotational

7 Fracture Mechanics of Solder Bumps During Ball Shear Testing: Effect of Bump Size Fig. 7. FEM mesh showing the solder bump rotation and uneven deformation field after 20 lm displacement. Dashed area indicates crack-tip location, and for better understanding of bump motion, arrows are added in this illustration. moment. Since plastic deformation and development of a rotational moment occurs concurrently, it is not possible to determine experimentally exactly how and when the rotation occurs. However, our FEM analysis indicates that the rotational moment develops even at the early stages of probe displacement. Figure 7, where FEM analysis of a 610 lm bump at 20 lm displacement is shown, highlights the development of the rotational moment. It can be seen that the FEM mesh rotates in the shearing direction, which is an indication of the body rotation in that direction. The result also shows that the deformation is more extensive in the upper half of the bump. The deformation constraint at the interface is responsible for the development of such an uneven deformation field and the development of force in the vertical direction. With the solder body anchored at the interface, this vertical force field creates the rotational moment in a bump body. The degree of bump rotation at a given time should be determined by the rotational moment, which in turn is determined by the magnitude of the vertical force and distance between the contact point and crack tip. Both of these quantities are impossible to quantify simultaneously during ball shear testing, but a qualitative prediction of the degree of body rotation can be made from the initial stand-free distance between the probe tip and the interface edge, DX in Fig. 1. This prediction is possible because DX determines the initial level of the rotational moment, that is, the larger the DX, the greater the degree of body rotation. Also this trend will remain the same throughout the entire displacement because a bump with a larger DX rotates more per given displacement and makes the crack grow even faster once it starts to propagate. Figure 8 presents the FEM calculation of stress intensity factors for various bump sizes and demonstrates the Fig. 8. Plot showing K I and K II developments at a crack tip with shear displacement (lm). For better recognition of the relationship between DX and crack growth rate and K I development, the DX value is also included in the legend. In this simulation, the crack is assumed to be 1 lm long and located at the corner of the IMC layer (Fig. 1). basis for faster crack initiation and propagation in larger bumps. The stress intensity factor calculation in Fig. 8 assumes the presence of identical 1 lm precracks at the interface. The result shows that K I always develops faster than K II for any given bump size. This is a direct result of body rotation and is consistent with our previous study in which the development of stress intensity factors is analyzed. 9 In addition, it can be seen that the K I development is far faster in larger bumps having longer DX, which should make the critical cracks grow faster in larger bumps. Therefore, it is reasonable to conclude that the more rapid crack growth shown in Fig. 2 for larger bumps results from a higher degree of bump body rotation and faster development of K I with displacement. DISCUSSION Ball shear testing is intended to be an easy and quantitative assessment of the interfacial integrity of solder joints, but our study reveals that the resulting data requires more thoughtful interpretation. In particular, the fact that fracture does not proceed by simple rigid shear but is accompanied by the concurrent processes of body rotation and bump deformation creates considerable complexity in relating the resulting force displacement data to valid fracture mechanics. For instance, the interface fracture strength cannot be determined from the AFF because it is contaminated by the force required for bump deformation at the probe contact. Thus, the error introduced into the AFF by the deformation force, may be responsible for the significant variation in fracture strength reported in previous studies, some of which are given in Table III, which presents a collection of fracture

8 Bang, Kim, Kang, and Oh Table III. Summary of Fracture Strength Data Reported in Previous Studies and Test Conditions Used in Those Studies Joint Tensile Fracture Strength a (MPa) Metallization Joint Thickness (mm) Joint Area Tensile Rate (mm/min) Lee and Chen Cu mm (diam.) 0.6 Prakash and Sritharan Cu mm Quan Cu mm Chen et al Ni-Au mm Ball Shear Fracture Strength a (MPa) Metallization Ball Diameter (mm) Pad Size (Diameter) (mm) Shear Rate (lm/s) This study 61 Cu Lee et al. 2,b Cu Zhang et al Cu Bang et al Cu Lee et al Cu Ni-Au 0.60 Yoon et al Ni-Au Chang and Chiang 6 54 Ni-Au Choi et al Ni-Au Peng et al Ni Data from both joint tensile tests (metallization/solder/metallization configuration) and ball shear tests (solder/metallization bump configuration) is shown. a The fracture is reported to take place generally at the interface area (IMC or solder near to IMC). Fracture strengths in this table are the values directly calculated from the raw fracture force data (AFF) divided by the interface area; b Lee et al. argued in their article that the variation of fracture strength data mainly originated from difference in solder microstructure between tested bumps. strength results from tensile and ball shear testing configurations. Note that four different studies report reasonably consistent values of the fracture strength from tensile tests, 80 MPa, in spite of significant variation in test details. On the other hand, studies of ball shear testing produce significantly scattered fracture strength values, ranging from 43 MPa to 86 MPa. According to our analysis, this is the result of the variation in deformation force due to differing bump size or bump geometry among those studies. The sensitivity of the AFF to bump size or bump geometry would significantly limit the usefulness of the ball shear test method because it would mean that valid comparisons can be made only when bumps have reasonably identical size and geometry. One possible resolution to this problem may be the use of a model, such as the one developed in this study, that allows an estimation of the contact deformation force (and thus an extraction of the true interfacial fracture force). As evidenced in Eq. 5, implementation of our model is fairly simple, as it only requires data on fracture displacement (U f ) and solder yield strength (r Y ). The determination of the fracture displacement is not a challenging task because it can be easily determined from the force displacement data. The yield strength cannot be determined directly from the force displacement data, although it can be extracted from data similar to that in Fig. 3, that is, bump diameter versus AFF. For practical application of the model, however, lack of bump diameter versus AFF data may not present a serious challenge. First of all, owing to extensive studies in this field, yield strength of various solder alloys are reasonably well known, and can be used in Eq. 5. Furthermore, in many cases, the yield strength can be assumed constant for all bumps being compared, so the interfacial fracture strength estimated by any reasonable choice of yield strength will allow comparative validity. The data shown in Table III and our estimation of interfacial strength, which ranges from 40 MPa to 48 MPa, present another critical implication for the practical use of ball shear testing. We believe that, when the interfacial fracture strengths presented in Table III are adjusted to account for the influence of deformation force on the AFF, the interfacial strength will be similar to the values obtained in our study. The value from our study is significantly lower than the interface fracture strength measured in the tensile test configuration, 80 MPa. Even the shear fracture strengths unadjusted for deformation

9 Fracture Mechanics of Solder Bumps During Ball Shear Testing: Effect of Bump Size force shown in Table III are generally lower than those measured in tensile tests. This result appears to suggest that the interfacial fracture strength varies with the method of characterization, and that the one measured by ball shear testing is significantly lower than the one measured by tensile testing. Because the fracture in both configurations is found to occur by the same crack-opening mode, they might be expected to yield similar values. However, it is our belief that this difference is the result of a difference in critical stress intensity factor for fracture (K c ) for the following reasons. 14,27 The test stress is evenly applied to the interface in tensile mode, while in bump shear testing, it is highly concentrated in the area near the rotational axis of the bump, which is a harsher condition. So, it is plausible to conclude that the critical stress intensity factor for fracture (K c ) is lower in the ball shear test than in the tensile test configuration. Therefore, the interfacial fracture strength measured by ball shear testing may have limited validity, as it simply reflects the lower K c. On the other hand, the fact that the integrity of the bump interface assessed by ball shear testing represents the worst-case scenario may make it the most meaningful for engineering purposes and of high value in the packaging industry. It is certain that fracture mechanics active in ball shear testing is better understood with the help of the experimental data and analysis done in the present work. However, there are a few areas that need further investigation to further improve our understanding and thus better utilize the ball shear test. One particular area of pressing importance appears to be the characterization related to cracking, such as the size and location of embryonic cracks, especially at the moment of fracture initiation. Presently, the cracking status of the interface prior to the AFF is unknown, yet it is important to investigate in order to determine the critical crack size for fracture in ball shear testing. Furthermore, our study fails to explain why the fracture displacement is fairly independent of bump size. Since greater and faster body rotation occurs in larger bumps, one would expect the fracture in larger bumps to require less probe displacement. It may be that the body rotation does not proceed much before a sizable crack occurs at the interface corner, and that crack nucleation at that site is delayed until displacement is nearly at the point of fracture. In that case, the fracture displacement may become relatively insensitive to the bump size, but this remains the subject of further investigation. CONCLUSION This paper investigates the influence of bump size on the fracture behavior of Pb-Sn solder bumps with identical interfacial area for the purpose of determining the factors affecting the fracture force and the crack growth kinetics. Experimentally, it is found that the ball shear testing result, that is, the force displacement curve, is affected greatly by the bump size even though all bumps have an identical interfacial area. The consistent result is that, with increasing bump size, the AFF increases while the rate of force drop per displacement decreases. Our analysis suggests that the size dependence of AFF exists because of the bump deformation at the probe contact. A large bump deforms more per given displacement and therefore demands a higher force to initiate fracture. Our study also suggests that the faster crack growth rate seen in larger bumps is related to the body rotation of the bump during shearing. With body rotation, the stress developing at the crack tip is not pure shear, but rather, includes a significant tensile component, which results in crack growth governed by the crackopening mode. Consequently, a crack in a larger bump propagates faster once it is initiated because a greater degree of body rotation makes K I develop faster. From these observations and related analysis, it is concluded that the true interfacial fracture strength can be determined only after a correction is made to account for deformation force. It is also concluded that the corrected interface fracture strength measured in ball shear testing represents the worst possible case because the mechanical constraint at the crack tip in conjunction with K I development due to body rotation facilitates crack formation and propagation. 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